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6t+i agent alternative at+i Bernheim & Whinston best response characterization coalition proof common agency game common agency model Consider continuation payoffs continuation values contribution equilibrium exists contribution of principal defined denoted deterministic difference dynamic coalition-proof equilibrium dynamic common agency dynamic game efficient equi equilibrium payoffs equivalent flow contribution flow marginal contribution follows given grand coalition greedy algorithm hence history ht inequality intertemporal job matching model librium marginal contribution equilibrium Markov Perfect Equilibrium Markov strategies Markovian maximizes modified program multi-armed bandit Nash equilibrium notion optimal action optimal policy payoff matrix payoff relevant perfect equilibria perfect information period players principal receives proof equilibrium Proof of Theorem realization renegotiation-proofness restriction reward function satisfied social value solution concept spot wages static common agency static game stochastic strategy profile subadditive subset sufficient condition task transferable utility truncated truthful strategies unique truthful equilibrium Valimaki vector weak superadditivity Whinston 1986a zero